The elections watchdog apologised for allowing Britain First to put 'Remember Lee Rigby' on voting slips in the European elections. Photograph: Matt Cardy/Getty

The elections watchdog has agreed to introduce new rules over the descriptions political parties can use after a review of its decision to allow an extremist group to adopt a slogan featuring murdered soldier Lee Rigby.

The Electoral Commission again apologised to the family of the murdered fusilier for allowing Britain First to put "Remember Lee Rigby" on voting slips in this month's European elections, and said it was tightening up its system of checks to ensure a similar mistake is never repeated.

Although the slogan cannot be used in future elections it can still feature on ballot papers at the European elections in Wales on 22 May, which take place on the first anniversary of Rigby's death. The 25-year-old father of one was killed near Woolwich barracks in south-east London.

The Electoral Commission chairwoman, Jenny Watson, apologised personally to members of Rigby's family in a series of "difficult and emotional calls".

The report of the independent review into the decision said: "It should be noted that each call confirmed that the use of Fusilier Rigby's name in a party description had caused deep offence and distress."

Britain First applied to use seven slogans in the elections and four were rejected, but the remaining three, including the slogan relating to Rigby, were approved by the watchdog.

The commission's director of party and election finance, Peter Horne, who resigned last week, "remembered thinking that it was distasteful but not sufficient to cause offence", the investigation said.

Although the review found the staff involved acted largely within the commission's processes, they failed to consider any need to protect public safety, morals or the rights and reputations of others.

Elizabeth Butler, who carried out the investigation, said the watchdog must introduce checks when personal names are used in party names or descriptions to ensure the individual or their family has consented, and review all names, descriptions and emblems currently on the register.

Butler, the independent chairwoman of the commission's audit committee, called on the watchdog to consider the wider context when approving party names and descriptions and involve more senior officials in the decision.

Watson said: "The Electoral Commission is deeply sorry for this mistake and the pain that it has caused Fusilier Rigby's family. The commission welcomes the report of the independent investigator and has accepted all the recommendations that have been made. These will now be implemented as quickly as possible to ensure a similar mistake is never repeated."